Question

Pls solve this fast.

Answer 1

Here is the solution :

According to the remainder theorem, If (x-a) is a factor of P(x), Then P(a) = 0,

Given that, the equation is,
ax^4 + bx³ + cx² +dx + e, Let this equation be equal to P(x)
=> P(x) = ax^4 + bx³ + cx² + dx + e,

Now according to the Question, x²-1 is a factor of P(x), Which means, P(1) and P(-1) must be equal to 0 [According to Remainder Theorem],

Because x²-1 must equal to 0 => x = √1 => x = either + 1 or -1,

Now substituting -1, in the P(x),[Remember keeping -1 or +1 in P(x) gives 0, According to Remainder Theroem],

=> P(-1) = 0,
=> a(-1)^4 + b(-1)³ +c(-1)² + d(-1) + e = 0,
=>a - b + c - d + e = 0,
=> a + c + e = b + d,

Therefore We proved it !

Hope you understand, Please ask if there are any doubts ! Merry Christmas !
Thanking you, Bunti 360 !

Answer 2

this answer is useful to you.